Metrisability of three-dimensional path geometries
Differential Geometry
2014-10-21 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
Given a projective structure on a three-dimensional manifold, we find explicit obstructions to the local existence of a Levi-Civita connection in the projective class. These obstructions are given by projectively invariant tensors algebraically constructed from the projective Weyl curvature. We show, by examples, that their vanishing is necessary but not sufficient for local metrisability.
Keywords
Cite
@article{arxiv.1408.2170,
title = {Metrisability of three-dimensional path geometries},
author = {Maciej Dunajski and Michael Eastwood},
journal= {arXiv preprint arXiv:1408.2170},
year = {2014}
}
Comments
19 pages. In this version we analyse the projective structures arising from Einstein-Weyl geometries and make several other minor modifications and additions